Simplify the following expression: $x = \dfrac{7z^2 - 77z + 168}{z - 8} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ x =\dfrac{7(z^2 - 11z + 24)}{z - 8} $ Then we factor the remaining polynomial: $z^2 {-11}z + {24} $ ${-8} {-3} = {-11}$ ${-8} \times {-3} = {24}$ $ (z {-8}) (z {-3}) $ This gives us a factored expression: $\dfrac{7(z {-8}) (z {-3})}{z - 8}$ We can divide the numerator and denominator by $(z + 8)$ on condition that $z \neq 8$ Therefore $x = 7(z - 3); z \neq 8$